Avoid 'variable uninitialized when used within its own initialization' warning.
[ginac.git] / ginac / utils.cpp
1 /** @file utils.cpp
2  *
3  *  Implementation of several small and furry utilities needed within GiNaC
4  *  but not of any interest to the user of the library. */
5
6 /*
7  *  GiNaC Copyright (C) 1999-2020 Johannes Gutenberg University Mainz, Germany
8  *
9  *  This program is free software; you can redistribute it and/or modify
10  *  it under the terms of the GNU General Public License as published by
11  *  the Free Software Foundation; either version 2 of the License, or
12  *  (at your option) any later version.
13  *
14  *  This program is distributed in the hope that it will be useful,
15  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
16  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
17  *  GNU General Public License for more details.
18  *
19  *  You should have received a copy of the GNU General Public License
20  *  along with this program; if not, write to the Free Software
21  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
22  */
23
24 #include "ex.h"
25 #include "numeric.h"
26 #include "utils.h"
27 #include "version.h"
28
29 namespace GiNaC {
30
31 /* Version information buried into the library */
32 const int version_major = GINACLIB_MAJOR_VERSION;
33 const int version_minor = GINACLIB_MINOR_VERSION;
34 const int version_micro = GINACLIB_MICRO_VERSION;
35
36
37 /** ctor for pole_error exception class. */
38 pole_error::pole_error(const std::string& what_arg, int degree)
39         : domain_error(what_arg), deg(degree) { }
40
41 /** Return the degree of the pole_error exception class. */
42 int pole_error::degree() const
43 {
44         return deg;
45 }
46
47 /** Integer binary logarithm */
48 unsigned log2(unsigned n)
49 {
50         unsigned k;
51         for (k = 0; n > 1; n >>= 1)
52                 ++k;
53         return k;
54 }
55
56 /** Compute the multinomial coefficient n!/(p1!*p2!*...*pk!) where
57  *  n = p1+p2+...+pk, i.e. p is a partition of n.
58  */
59 const numeric
60 multinomial_coefficient(const std::vector<unsigned> & p)
61 {
62         numeric n = 0, d = 1;
63         for (auto & it : p) {
64                 n = n.add(numeric(it));
65                 d = d.mul(factorial(numeric(it)));
66         }
67         return factorial(n).div(d);
68 }
69
70
71 /** How many static objects were created?  Only the first one must create
72  *  the static flyweights on the heap. */
73 int library_init::count = 0;
74
75 /** Ctor of static initialization helpers.  The fist call to this is going
76  *  to initialize the library, the others do nothing. */
77 library_init::library_init()
78 {
79         if (count++==0) {
80                 _num_120_p = (const numeric *)&dynallocate<numeric>(-120);
81                 _num_60_p = (const numeric *)&dynallocate<numeric>(-60);
82                 _num_48_p = (const numeric *)&dynallocate<numeric>(-48);
83                 _num_30_p = (const numeric *)&dynallocate<numeric>(-30);
84                 _num_25_p = (const numeric *)&dynallocate<numeric>(-25);
85                 _num_24_p = (const numeric *)&dynallocate<numeric>(-24);
86                 _num_20_p = (const numeric *)&dynallocate<numeric>(-20);
87                 _num_18_p = (const numeric *)&dynallocate<numeric>(-18);
88                 _num_15_p = (const numeric *)&dynallocate<numeric>(-15);
89                 _num_12_p = (const numeric *)&dynallocate<numeric>(-12);
90                 _num_11_p = (const numeric *)&dynallocate<numeric>(-11);
91                 _num_10_p = (const numeric *)&dynallocate<numeric>(-10);
92                 _num_9_p = (const numeric *)&dynallocate<numeric>(-9);
93                 _num_8_p = (const numeric *)&dynallocate<numeric>(-8);
94                 _num_7_p = (const numeric *)&dynallocate<numeric>(-7);
95                 _num_6_p = (const numeric *)&dynallocate<numeric>(-6);
96                 _num_5_p = (const numeric *)&dynallocate<numeric>(-5);
97                 _num_4_p = (const numeric *)&dynallocate<numeric>(-4);
98                 _num_3_p = (const numeric *)&dynallocate<numeric>(-3);
99                 _num_2_p = (const numeric *)&dynallocate<numeric>(-2);
100                 _num_1_p = (const numeric *)&dynallocate<numeric>(-1);
101                 _num_1_2_p = (const numeric *)&dynallocate<numeric>(-1,2);
102                 _num_1_3_p = (const numeric *)&dynallocate<numeric>(-1,3);
103                 _num_1_4_p = (const numeric *)&dynallocate<numeric>(-1,4);
104                 _num0_p = (const numeric *)&dynallocate<numeric>(0);
105                 _num0_bp  = _num0_p;  // Cf. class ex default ctor.
106                 _num1_4_p = (const numeric *)&dynallocate<numeric>(1,4);
107                 _num1_3_p = (const numeric *)&dynallocate<numeric>(1,3);
108                 _num1_2_p = (const numeric *)&dynallocate<numeric>(1,2);
109                 _num1_p = (const numeric *)&dynallocate<numeric>(1);
110                 _num2_p = (const numeric *)&dynallocate<numeric>(2);
111                 _num3_p = (const numeric *)&dynallocate<numeric>(3);
112                 _num4_p = (const numeric *)&dynallocate<numeric>(4);
113                 _num5_p = (const numeric *)&dynallocate<numeric>(5);
114                 _num6_p = (const numeric *)&dynallocate<numeric>(6);
115                 _num7_p = (const numeric *)&dynallocate<numeric>(7);
116                 _num8_p = (const numeric *)&dynallocate<numeric>(8);
117                 _num9_p = (const numeric *)&dynallocate<numeric>(9);
118                 _num10_p = (const numeric *)&dynallocate<numeric>(10);
119                 _num11_p = (const numeric *)&dynallocate<numeric>(11);
120                 _num12_p = (const numeric *)&dynallocate<numeric>(12);
121                 _num15_p = (const numeric *)&dynallocate<numeric>(15);
122                 _num18_p = (const numeric *)&dynallocate<numeric>(18);
123                 _num20_p = (const numeric *)&dynallocate<numeric>(20);
124                 _num24_p = (const numeric *)&dynallocate<numeric>(24);
125                 _num25_p = (const numeric *)&dynallocate<numeric>(25);
126                 _num30_p = (const numeric *)&dynallocate<numeric>(30);
127                 _num48_p = (const numeric *)&dynallocate<numeric>(48);
128                 _num60_p = (const numeric *)&dynallocate<numeric>(60);
129                 _num120_p = (const numeric *)&dynallocate<numeric>(120);
130
131                 new((void*)&_ex_120) ex(*_num_120_p);
132                 new((void*)&_ex_60) ex(*_num_60_p);
133                 new((void*)&_ex_48) ex(*_num_48_p);
134                 new((void*)&_ex_30) ex(*_num_30_p);
135                 new((void*)&_ex_25) ex(*_num_25_p);
136                 new((void*)&_ex_24) ex(*_num_24_p);
137                 new((void*)&_ex_20) ex(*_num_20_p);
138                 new((void*)&_ex_18) ex(*_num_18_p);
139                 new((void*)&_ex_15) ex(*_num_15_p);
140                 new((void*)&_ex_12) ex(*_num_12_p);
141                 new((void*)&_ex_11) ex(*_num_11_p);
142                 new((void*)&_ex_10) ex(*_num_10_p);
143                 new((void*)&_ex_9) ex(*_num_9_p);
144                 new((void*)&_ex_8) ex(*_num_8_p);
145                 new((void*)&_ex_7) ex(*_num_7_p);
146                 new((void*)&_ex_6) ex(*_num_6_p);
147                 new((void*)&_ex_5) ex(*_num_5_p);
148                 new((void*)&_ex_4) ex(*_num_4_p);
149                 new((void*)&_ex_3) ex(*_num_3_p);
150                 new((void*)&_ex_2) ex(*_num_2_p);
151                 new((void*)&_ex_1) ex(*_num_1_p);
152                 new((void*)&_ex_1_2) ex(*_num_1_2_p);
153                 new((void*)&_ex_1_3) ex(*_num_1_3_p);
154                 new((void*)&_ex_1_4) ex(*_num_1_4_p);
155                 new((void*)&_ex0) ex(*_num0_p);
156                 new((void*)&_ex1_4) ex(*_num1_4_p);
157                 new((void*)&_ex1_3) ex(*_num1_3_p);
158                 new((void*)&_ex1_2) ex(*_num1_2_p);
159                 new((void*)&_ex1) ex(*_num1_p);
160                 new((void*)&_ex2) ex(*_num2_p);
161                 new((void*)&_ex3) ex(*_num3_p);
162                 new((void*)&_ex4) ex(*_num4_p);
163                 new((void*)&_ex5) ex(*_num5_p);
164                 new((void*)&_ex6) ex(*_num6_p);
165                 new((void*)&_ex7) ex(*_num7_p);
166                 new((void*)&_ex8) ex(*_num8_p);
167                 new((void*)&_ex9) ex(*_num9_p);
168                 new((void*)&_ex10) ex(*_num10_p);
169                 new((void*)&_ex11) ex(*_num11_p);
170                 new((void*)&_ex12) ex(*_num12_p);
171                 new((void*)&_ex15) ex(*_num15_p);
172                 new((void*)&_ex18) ex(*_num18_p);
173                 new((void*)&_ex20) ex(*_num20_p);
174                 new((void*)&_ex24) ex(*_num24_p);
175                 new((void*)&_ex25) ex(*_num25_p);
176                 new((void*)&_ex30) ex(*_num30_p);
177                 new((void*)&_ex48) ex(*_num48_p);
178                 new((void*)&_ex60) ex(*_num60_p);
179                 new((void*)&_ex120) ex(*_num120_p);
180
181                 // Initialize print context class info (this is not strictly necessary
182                 // but we do it anyway to make print_context_class_info::dump_hierarchy()
183                 // output the whole hierarchy whether or not the classes are actually
184                 // used)
185                 print_context::get_class_info_static();
186                 print_dflt::get_class_info_static();
187                 print_latex::get_class_info_static();
188                 print_python::get_class_info_static();
189                 print_python_repr::get_class_info_static();
190                 print_tree::get_class_info_static();
191                 print_csrc::get_class_info_static();
192                 print_csrc_float::get_class_info_static();
193                 print_csrc_double::get_class_info_static();
194                 print_csrc_cl_N::get_class_info_static();
195         }
196 }
197
198
199 /** Dtor of static initialization helpers.  The last call to this is going
200  *  to shut down the library, the others do nothing. */
201 library_init::~library_init()
202 {
203         if (--count==0) {
204                 // It's really necessary to clean up, since the program
205                 // lifetime might not be the same as libginac.{so,dll} one
206                 // (e.g. consider // dlopen/dlsym/dlclose sequence).
207                 // Let the ex dtors care for deleting the numerics!
208                 _ex120.~ex();
209                 _ex_120.~ex();
210                 _ex60.~ex();
211                 _ex_60.~ex();
212                 _ex48.~ex();
213                 _ex_48.~ex();
214                 _ex30.~ex();
215                 _ex_30.~ex();
216                 _ex25.~ex();
217                 _ex_25.~ex();
218                 _ex24.~ex();
219                 _ex_24.~ex();
220                 _ex20.~ex();
221                 _ex_20.~ex();
222                 _ex18.~ex();
223                 _ex_18.~ex();
224                 _ex15.~ex();
225                 _ex_15.~ex();
226                 _ex12.~ex();
227                 _ex_12.~ex();
228                 _ex11.~ex();
229                 _ex_11.~ex();
230                 _ex10.~ex();
231                 _ex_10.~ex();
232                 _ex9.~ex();
233                 _ex_9.~ex();
234                 _ex8.~ex();
235                 _ex_8.~ex();
236                 _ex7.~ex();
237                 _ex_7.~ex();
238                 _ex6.~ex();
239                 _ex_6.~ex();
240                 _ex5.~ex();
241                 _ex_5.~ex();
242                 _ex4.~ex();
243                 _ex_4.~ex();
244                 _ex3.~ex();
245                 _ex_3.~ex();
246                 _ex2.~ex();
247                 _ex_2.~ex();
248                 _ex1.~ex();
249                 _ex_1.~ex();
250                 _ex1_2.~ex();
251                 _ex_1_2.~ex();
252                 _ex1_3.~ex();
253                 _ex_1_3.~ex();
254                 _ex1_4.~ex();
255                 _ex_1_4.~ex();
256                 _ex0.~ex();
257         }
258 }
259
260 void library_init::init_unarchivers() { }
261
262
263 //////////
264 // Flyweight chest of numbers is re-initialized here. Note that this works
265 // because the numeric* have been dynallocated by the library_init ctor before
266 // (with the first module that has a static library_init object), so the
267 // assignments here only increment their refcounts.
268 //////////
269
270 // static numeric -120
271 const numeric *_num_120_p;
272 const ex _ex_120 = ex(*_num_120_p);
273
274 // static numeric -60
275 const numeric *_num_60_p;
276 const ex _ex_60 = ex(*_num_60_p);
277
278 // static numeric -48
279 const numeric *_num_48_p;
280 const ex _ex_48 = ex(*_num_48_p);
281
282 // static numeric -30
283 const numeric *_num_30_p;
284 const ex _ex_30 = ex(*_num_30_p);
285
286 // static numeric -25
287 const numeric *_num_25_p;
288 const ex _ex_25 = ex(*_num_25_p);
289
290 // static numeric -24
291 const numeric *_num_24_p;
292 const ex _ex_24 = ex(*_num_24_p);
293
294 // static numeric -20
295 const numeric *_num_20_p;
296 const ex _ex_20 = ex(*_num_20_p);
297
298 // static numeric -18
299 const numeric *_num_18_p;
300 const ex _ex_18 = ex(*_num_18_p);
301
302 // static numeric -15
303 const numeric *_num_15_p;
304 const ex _ex_15 = ex(*_num_15_p);
305
306 // static numeric -12
307 const numeric *_num_12_p;
308 const ex _ex_12 = ex(*_num_12_p);
309
310 // static numeric -11
311 const numeric *_num_11_p;
312 const ex _ex_11 = ex(*_num_11_p);
313
314 // static numeric -10
315 const numeric *_num_10_p;
316 const ex _ex_10 = ex(*_num_10_p);
317
318 // static numeric -9
319 const numeric *_num_9_p;
320 const ex _ex_9 = ex(*_num_9_p);
321
322 // static numeric -8
323 const numeric *_num_8_p;
324 const ex _ex_8 = ex(*_num_8_p);
325
326 // static numeric -7
327 const numeric *_num_7_p;
328 const ex _ex_7 = ex(*_num_7_p);
329
330 // static numeric -6
331 const numeric *_num_6_p;
332 const ex _ex_6 = ex(*_num_6_p);
333
334 // static numeric -5
335 const numeric *_num_5_p;
336 const ex _ex_5 = ex(*_num_5_p);
337
338 // static numeric -4
339 const numeric *_num_4_p;
340 const ex _ex_4 = ex(*_num_4_p);
341
342 // static numeric -3
343 const numeric *_num_3_p;
344 const ex _ex_3 = ex(*_num_3_p);
345
346 // static numeric -2
347 const numeric *_num_2_p;
348 const ex _ex_2 = ex(*_num_2_p);
349
350 // static numeric -1
351 const numeric *_num_1_p;
352 const ex _ex_1 = ex(*_num_1_p);
353
354 // static numeric -1/2
355 const numeric *_num_1_2_p;
356 const ex _ex_1_2= ex(*_num_1_2_p);
357
358 // static numeric -1/3
359 const numeric *_num_1_3_p;
360 const ex _ex_1_3= ex(*_num_1_3_p);
361
362 // static numeric -1/4
363 const numeric *_num_1_4_p;
364 const ex _ex_1_4= ex(*_num_1_4_p);
365
366 // static numeric 0
367 const numeric *_num0_p;
368 const basic *_num0_bp;
369 const ex _ex0 = ex(*_num0_p);
370
371 // static numeric 1/4
372 const numeric *_num1_4_p;
373 const ex _ex1_4 = ex(*_num1_4_p);
374
375 // static numeric 1/3
376 const numeric *_num1_3_p;
377 const ex _ex1_3 = ex(*_num1_3_p);
378
379 // static numeric 1/2
380 const numeric *_num1_2_p;
381 const ex _ex1_2 = ex(*_num1_2_p);
382
383 // static numeric 1
384 const numeric *_num1_p;
385 const ex _ex1 = ex(*_num1_p);
386
387 // static numeric 2
388 const numeric *_num2_p;
389 const ex _ex2 = ex(*_num2_p);
390
391 // static numeric 3
392 const numeric *_num3_p;
393 const ex _ex3 = ex(*_num3_p);
394
395 // static numeric 4
396 const numeric *_num4_p;
397 const ex _ex4 = ex(*_num4_p);
398
399 // static numeric 5
400 const numeric *_num5_p;
401 const ex _ex5 = ex(*_num5_p);
402
403 // static numeric 6
404 const numeric *_num6_p;
405 const ex _ex6 = ex(*_num6_p);
406
407 // static numeric 7
408 const numeric *_num7_p;
409 const ex _ex7 = ex(*_num7_p);
410
411 // static numeric 8
412 const numeric *_num8_p;
413 const ex _ex8 = ex(*_num8_p);
414
415 // static numeric 9
416 const numeric *_num9_p;
417 const ex _ex9 = ex(*_num9_p);
418
419 // static numeric 10
420 const numeric *_num10_p;
421 const ex _ex10 = ex(*_num10_p);
422
423 // static numeric 11
424 const numeric *_num11_p;
425 const ex _ex11 = ex(*_num11_p);
426
427 // static numeric 12
428 const numeric *_num12_p;
429 const ex _ex12 = ex(*_num12_p);
430
431 // static numeric 15
432 const numeric *_num15_p;
433 const ex _ex15 = ex(*_num15_p);
434
435 // static numeric 18
436 const numeric *_num18_p;
437 const ex _ex18 = ex(*_num18_p);
438
439 // static numeric 20
440 const numeric *_num20_p;
441 const ex _ex20 = ex(*_num20_p);
442
443 // static numeric 24
444 const numeric *_num24_p;
445 const ex _ex24 = ex(*_num24_p);
446
447 // static numeric 25
448 const numeric *_num25_p;
449 const ex _ex25 = ex(*_num25_p);
450
451 // static numeric 30
452 const numeric *_num30_p;
453 const ex _ex30 = ex(*_num30_p);
454
455 // static numeric 48
456 const numeric *_num48_p;
457 const ex _ex48 = ex(*_num48_p);
458
459 // static numeric 60
460 const numeric *_num60_p;
461 const ex _ex60 = ex(*_num60_p);
462
463 // static numeric 120
464 const numeric *_num120_p;
465 const ex _ex120 = ex(*_num120_p);
466
467 // comment skeleton for header files
468
469
470 // member functions
471
472         // default constructor, destructor, copy constructor and assignment operator
473         // none
474
475         // other constructors
476         // none
477
478         // functions overriding virtual functions from base classes
479         // none
480         
481         // new virtual functions which can be overridden by derived classes
482         // none
483
484         // non-virtual functions in this class
485         // none
486
487 // member variables
488 // none
489         
490
491
492 // comment skeleton for implementation files
493
494
495 //////////
496 // default constructor, destructor, copy constructor and assignment operator
497 //////////
498
499 // public
500 // protected
501
502 //////////
503 // other constructors
504 //////////
505
506 // public
507 // none
508
509 //////////
510 // functions overriding virtual functions from base classes
511 //////////
512
513 // public
514 // protected
515 // none
516
517 //////////
518 // new virtual functions which can be overridden by derived classes
519 //////////
520
521 // public
522 // protected
523 // none
524
525 //////////
526 // non-virtual functions in this class
527 //////////
528
529 // public
530 // protected
531 // none
532
533 //////////
534 // static member variables
535 //////////
536
537 // protected
538 // private
539 // none
540
541
542 } // namespace GiNaC